U.S carriers don't have much surge capacity. It's not like DL keeps 100 753s sitting around waiting to sub for MD-88s or 738s when weather turns bad. It's not just a matter of extra pilots, either: the pilots need to be where the planes wind up, and qualified on those aircraft.
The U.S. airport network, in a lot of busy hubs, doesn't have much surge capacity, either. It's not like LaGuardia can just start handling 110 departures an hour when the weather clears up and the runsways are ready.
The 'solution' for the passengers on the fully booked flights the OP abandoned is to hope they just don't want to fly in really bad weather. Refund their tickets, or push them into the few empty seats next week.
Nobody wants to pay for a regulatory mandate, something of the form that airlines couldn't sell more than 85% of the seats on any scheduled flight until 24 hours before departure to ensure that there will be seats in the event of flight cancellations from crew absence, mechanicals, or weather. (U.S. state utility regulators routinely demand comparable available surplus for electrical generation capacity, btw, and consumers pay for it in the the rate structures.)
Compare Delta's efforts and performance to JetBlue circa 2014:
We just won't even try.
http://www.usatoday.com/story/todayi...tdown/4361203/
JetBlue Airways defended its decision to shut down operations at four major airports for 17 hours this week but said it would compensate the most inconvenienced customers.
In a conference call with reporters Wednesday afternoon, JetBlue's Chief Operating Officer Rob Maruster said the airline decided to suspend almost all flights to protect its aircraft and personnel from freezing temperatures and potential icy conditions on the ground.
The airline grounded almost all planes at New York's JFK and LaGuardia, Newark's Liberty International and Boston's Logan airports from 5 p.m. Monday until 10 a.m. Tuesday morning.